Mechanics PYQ — Page 4

The mechanical quantity, which has dimensions of reciprocal of mass $\left(\mathrm{M}^{-1}\right)$ is

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:

A particle moves with a velocity $(5 \hat{i}-3 \hat{j}+6 \hat{k}) \mathrm{ms}^{-1}$ horizontally under the action of constant force $(10 \hat{i}+10 \hat{j}+20 \hat{k}) \mathrm{N}$. The instantaneous power supplied to the particle is:

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $4m{s}^{-1}$. The ball strikes the water surface after $4s$. The height of bridge above water surface is (Take $g=10m{s}^{-2}$):

A bullet from a gun is fired on a rectangular wooden block with velocity $u$. When bullet travels $24\mathrm{cm}$ through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is :

A metal wire has mass ($0.4\pm 0.002$) $g$, radius ($0.3\pm 0.001$) $\mathrm{mm}$ and length ($5\pm 0.02$) $\mathrm{cm}$. The maximum possible percentage error in the measurement of density will nearly be:

Two particles $A$ and $B$ initially at rest, move towards each other under mutual force of attraction. At an instance when the speed of $A$ is $v$ and speed of $B$ is $3 v$, the speed of centre of mass is

A satellite is orbiting just above the surface of the earth with period $T$. If $d$ is the density of the earth and $G$ is the universal constant of gravitation, the quantity $\frac{3\pi }{Gd}$ represents :

If the kinetic energy of a body becomes four times, its momentum becomes

The dimensions $[\mathrm{MLT}{A-2}^{-2}]$ belong to the

The position-time $(x-t)$ graph for positive acceleration is:

The percentage error in the measurement of $g$ is $\left(\right.$ Given that $g=\frac{4 \pi^2 \mathrm{~L}}{\mathrm{~T}^2}, \mathrm{~L}=(10 \pm 0.1) \mathrm{cm}$, $\mathrm{T}=(100 \pm 1) \mathrm{s}):$

If $\overrightarrow{\mathrm{F}}=2 \hat{i}+\hat{j}-\hat{k}$ and $\vec{r}=3 \hat{i}+2 \hat{j}-2 \hat{k}$, then the scalar and vector products of $\vec{F}$ and $\vec{r}$ have the magnitudes respectively as:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R), Assertion (A): When a fire cracker (rocket) explodes in mid air, its fragments fly in such a way that they continue moving in the same path, which the fire cracker would have followed, had it not exploded Reason (R): Explosion of cracker (rocket) occurs due to internal forces only and no external force acts for this explosion. In the light of the above statements, choose the most appropriate answer from the options given below:

Match List - I with List - II : <table class="pyq-table"><tbody><tr><td colspan="2" rowspan="1">List - I</td><td colspan="2" rowspan="1">List - II</td></tr><tr><td>(a)</td><td>Gravitational constant (G)</td><td>(i)</td><td>$[{L}^{2}{T}^{-2}]$</td></tr><tr><td>(b)</td><td>Gravitational potential energy</td><td>(ii)</td><td>$[{M}^{-1}{L}^{3}{T}^{-2}]$</td></tr><tr><td>(c)</td><td>Gravitational potential</td><td>(iii)</td><td>$[{\mathrm{LT}}^{-2}]$</td></tr><tr><td>(d)</td><td>Gravitational intensity</td><td>(iv)</td><td>$[{\mathrm{ML}}^{2}{T}^{-2}]$</td></tr></tbody></table>Choose the correct answer from the options given below:

The distance covered by a body of mass $5 \mathrm{~g}$ having linear momentum $0.3 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$ in $5 \mathrm{~s}$ is:

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2:2:1$. If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$, the speed of the third (lighter) fragment is:

An electric lift with a maximum load of $2000\mathrm{kg}$ (lift $+$ passengers) is moving up with a constant speed of $1.5{ms}^{-1}$. The frictional force opposing the motion is $3000N$. The minimum power delivered by the motor to the lift in watts is : $(g=10{ms}^{-2})$

Two copper vessels $A$ and $B$ have the same base area but of different shapes. A takes twice the volume of water as that $B$ requires to fill upto a particular common height. Then the correct statement among the following is:

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the $x$-axis as shown in the figure. The ratio of their respective velocity is: 

A cricket ball is thrown by a player at a speed of $20 \mathrm{~m} / \mathrm{s}$ in a direction $30^{\circ}$ above the horizontal. The maximum height attained by the ball during its motion is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$ :

A gravitational field is present in a region and a mass is shifted from $A$ to $B$ through different paths as shown. If $W_1, W_2$ and $W_3$ represent the work done by the gravitational force along the respective paths, then 

The physical quantity that has the same dimensional formula as pressure is: